Locating Edge Domination Number of Some Classes of Claw-Free Cubic Graphs

Let G=<mfenced open="(" close=")">V;E</mfenced> be a simple graph with vertex set V and edge set E . In a graph G , a subset of edges denoted by M is referred to as an edge-dominating set of G if every edge that is not in M is incident to at least one member of M . A set M⊆E is the locating edge-dominating set if for every two edges e1,e2∈<mfenced open="(" close=")">E−M</mfenced> , the sets N<mfenced open="(" close=")">e1</mfenced>∩M and N<mfenced open="(" close=")">e2</mfenced>∩M are nonempty and different. The edge domination number γL<mfenced open="(" close=")">G</mfenced> of G is the minimum cardinality of all edge-dominating sets of G . The purpose of this study is to determine the locating edge domination number of certain types of claw-free cubic graphs.